Rapid Accelerometer Measurements of Vehicle Bumps at Bridge Approaches

2015 ◽  
Vol 2528 (1) ◽  
pp. 1-8
Author(s):  
Yuchuan Du ◽  
Chenglong Liu ◽  
Xi Zhang ◽  
Lijun Sun
Keyword(s):  
Linear Time ◽  
Evaluation Model ◽  
Field Tests ◽  
Small Scale ◽  
Linear Time Invariant ◽  
Structural Deterioration ◽  
Power Spectral ◽  
Bridge Structures ◽  
The Stability ◽  
The Impact

Bridge approach settlement (BAS) is one of the most common problems in highway and bridge construction. The settlement can result in unsafe driving conditions, rider discomfort, structural deterioration of bridges, and long-term maintenance costs. BAS research has focused mainly on causes, hazards, and countermeasures, with little emphasis on BAS measurement. This paper presents a rapid vehicle-mounted accelerometer method for BAS measurement and proposes a comprehensive BAS measure consisting of three indexes that measure user physical and psychological comfort as well as the impact on bridge structures. A wavelet transform is used to identify the reaction position. Power spectral density analysis and one-third octave band filtering are applied to calculate the weighted root mean square acceleration as an index of comfort. Adopting the annoyance rate concept from experimental psychology, an annoyance rate model was developed that includes a membership function and the distribution of user comfort levels. A quarter-car model and a linear time invariant (LTI) system were used to estimate the equivalent impact coefficient as an index of durability. Furthermore, a collective system equipped with z-axis accelerometers and a GPS device was created, and small-scale field tests were conducted in Shanghai, China. A velocity correction equation was generated to correct the evaluation model. The test results demonstrate the stability and efficiency of the rapid measurement system.

Coupled Stability of Multiport Systems—Theory and Experiments

1994 ◽  
Vol 116 (3) ◽  
pp. 419-428 ◽  
Author(s):  
J. E. Colgate
Keyword(s):  
Stability Property ◽  
Force Feedback ◽  
Linear Time ◽  
Experimental Studies ◽  
Sufficient Conditions ◽  
Direct Drive ◽  
Property A ◽  
Linear Time Invariant ◽  
The Stability ◽  
Necessary And Sufficient

This paper presents both theoretical and experimental studies of the stability of dynamic interaction between a feedback controlled manipulator and a passive environment. Necessary and sufficient conditions for “coupled stability”—the stability of a linear, time-invariant n-port (e.g., a robot, linearized about an operating point) coupled to a passive, but otherwise arbitrary, environment—are presented. The problem of assessing coupled stability for a physical system (continuous time) with a discrete time controller is then addressed. It is demonstrated that such a system may exhibit the coupled stability property; however, analytical, or even inexpensive numerical conditions are difficult to obtain. Therefore, an approximate condition, based on easily computed multivariable Nyquist plots, is developed. This condition is used to analyze two controllers implemented on a two-link, direct drive robot. An impedance controller demonstrates that a feedback controlled manipulator may satisfy the coupled stability property. A LQG/LTR controller illustrates specific consequences of failure to meet the coupled stability criterion; it also illustrates how coupled instability may arise in the absence of force feedback. Two experimental procedures—measurement of endpoint admittance and interaction with springs and masses—are introduced and used to evaluate the above controllers. Theoretical and experimental results are compared.

Kernel and Offspring Concepts for the Stability Robustness of Multiple Time Delayed Systems (MTDS)

2006 ◽  
Vol 129 (3) ◽  
pp. 245-251 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Time Delays ◽  
Linear Time ◽  
Characteristic Root ◽  
Invariance Property ◽  
Multiple Time ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Characteristic Roots ◽  
Stability Robustness ◽  
The Stability

A novel treatment for the stability of linear time invariant (LTI) systems with rationally independent multiple time delays is presented in this paper. The independence of delays makes the problem much more challenging compared to systems with commensurate time delays (where the delays have rational relations). We uncover some wonderful features for such systems. For instance, all the imaginary characteristic roots of these systems can be found exhaustively along a set of surfaces in the domain of the delays. They are called the “kernel” surfaces (curves for two-delay cases), and it is proven that the number of the kernel surfaces is manageably small and bounded. All possible time delay combinations, which yield an imaginary characteristic root, lie either on this kernel or its infinitely many “offspring” surfaces. Another hidden feature is that the root tendencies along these surfaces exhibit an invariance property. From these outstanding characteristics an efficient, exact, and exhaustive methodology results for the stability assessment. As an added uniqueness of this method, the systems under consideration do not have to be stable for zero delays. Several example case studies are presented, which are prohibitively difficult, if not impossible to solve using any other peer methodology known to the authors.

Stability Analysis of Multiple Time Delayed Systems Using the Direct Method

2003 ◽  
Author(s):  
Rifat Sipahi ◽  
Nejat Olgac
Keyword(s):  
Stability Analysis ◽  
Time Delays ◽  
Linear Time ◽  
Direct Method ◽  
Multiple Time ◽  
Delayed Systems ◽  
Practical Applications ◽  
Linear Time Invariant ◽  
Multiple Time Delays ◽  
The Stability

A novel treatment for the stability of a class of linear time invariant (LTI) systems with rationally independent multiple time delays using the Direct Method (DM) is studied. Since they appear in many practical applications in the systems and control community, this class of dynamics has attracted considerable interest. The stability analysis is very complex because of the infinite dimensional nature (even for single delay) of the dynamics and furthermore the multiplicity of these delays. The stability problem is much more challenging compared to the TDS with commensurate time delays (where time delays have rational relations). It is shown in an earlier publication of the authors that the DM brings a unique, exact and structured methodology for the stability analysis of commensurate time delayed cases. The transition from the commensurate time delays to multiple delay case motivates our study. It is shown that the DM reveals all possible stability regions in the space of multiple time delays. The systems that are considered do not have to possess stable behavior for zero delays. We present a numerical example on a system, which is considered “prohibitively difficult” in the literature, just to exhibit the strengths of the new procedure.

scholarly journals Torsion Discriminance for Stability of Linear Time-Invariant Systems

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 386
Author(s):  
Yuxin Wang ◽  
Huafei Sun ◽  
Yueqi Cao ◽  
Shiqiang Zhang
Keyword(s):  
Lebesgue Measure ◽  
Linear Time ◽  
Zero Solution ◽  
Positive Lebesgue Measure ◽  
Asymptotically Stable ◽  
Linear Time Invariant ◽  
Measurable Set ◽  
Linear Time Invariant Systems ◽  
The Stability ◽  
Time Invariant

This paper extends the former approaches to describe the stability of n-dimensional linear time-invariant systems via the torsion τ ( t ) of the state trajectory. For a system r ˙ ( t ) = A r ( t ) where A is invertible, we show that (1) if there exists a measurable set E 1 with positive Lebesgue measure, such that r ( 0 ) ∈ E 1 implies that lim t → + ∞ τ ( t ) ≠ 0 or lim t → + ∞ τ ( t ) does not exist, then the zero solution of the system is stable; (2) if there exists a measurable set E 2 with positive Lebesgue measure, such that r ( 0 ) ∈ E 2 implies that lim t → + ∞ τ ( t ) = + ∞ , then the zero solution of the system is asymptotically stable. Furthermore, we establish a relationship between the ith curvature ( i = 1 , 2 , ⋯ ) of the trajectory and the stability of the zero solution when A is similar to a real diagonal matrix.

Admissible Range of Proportional Gain in Stabilizing PID Region

2014 ◽  
Vol 530-531 ◽  
pp. 1068-1077 ◽  
Author(s):  
Yu Dong
Keyword(s):  
Linear Time ◽  
Stability Boundary ◽  
Closed Loop System ◽  
Double Pole ◽  
Linear Time Invariant ◽  
Admissible Range ◽  
Boundary Locus ◽  
The Stability ◽  
Time Invariant ◽  
Integral Gain

This paper considers the problem of stabilizing linear time-invariant plants by a PID controller. If the proportional gain reaches the extreme value, the closed-loop system contains a double pole on the imaginary axis. Using this property, the admissible range of the proportional gain is derived, also the corresponding integral gain and derivative gain are obtained. If the proportional gain is fixed, the stability region in the plane with respect to the integral gain and the derivative gain is determined by plotting the stability boundary locus. The effectiveness of the method presented is illustrated by several examples.

scholarly journals Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear Transformation

2011 ◽  
Vol 62 (1) ◽  
pp. 44-48 ◽  
Author(s):  
Paknosh Karimaghaee ◽  
Navid Noroozi
Keyword(s):  
Discrete Time ◽  
Closed Loop ◽  
Linear Time ◽  
Order Reduction ◽  
Bilinear Transformation ◽  
Reduced Order ◽  
Linear Time Invariant ◽  
The Stability ◽  
Controllability And Observability ◽  
Time Invariant

Frequency Weighted Discrete-Time Controller Order Reduction Using Bilinear TransformationThis paper addresses a new method for order reduction of linear time invariant discrete-time controller. This method leads to a new algorithm for controller reduction when a discrete time controller is used to control a continuous time plant. In this algorithm, at first, a full order controller is designed ins-plane. Then, bilinear transformation is applied to map the closed loop system toz-plane. Next, new closed loop controllability and observability grammians are calculated inz-plane. Finally, balanced truncation idea is used to reduce the order of controller. The stability property of the reduced order controller is discussed. To verify the effectiveness of our method, a reduced controller is designed for four discs system.

Equivalency of Stability Transitions Between the SDS (Spectral Delay Space) and DS (Delay Space)

2013 ◽  
Author(s):  
Qingbin Gao ◽  
Umut Zalluhoglu ◽  
Nejat Olgac
Keyword(s):  
Linear Time ◽  
Broad Class ◽  
Delay Systems ◽  
Multiple Delays ◽  
Delayed Systems ◽  
Linear Time Invariant ◽  
Time In Literature ◽  
The Stability ◽  
Time Invariant ◽  
Delay Space

It has been shown that the stability of LTI time-delayed systems with respect to the delays can be analyzed in two equivalent domains: (i) delay space (DS) and (ii) spectral delay space (SDS). Considering a broad class of linear time-invariant time delay systems with multiple delays, the equivalency of the stability transitions along the transition boundaries is studied in both spaces. For this we follow two corresponding radial lines in DS and SDS, and prove for the first time in literature that they are equivalent. This property enables us to extract local stability transition features within the SDS without going back to the DS. The main advantage of remaining in SDS is that, one can avoid a non-linear transition from kernel hypercurves to offspring hypercurves in DS. Instead the potential stability switching curves in SDS are generated simply by stacking a finite dimensional cube called the building block (BB) along the axes. A case study is presented within the report to visualize this property.

scholarly journals On the finite Fourier transforms of functions with infinite discontinuities

2002 ◽  
Vol 30 (5) ◽  
pp. 301-317
Author(s):  
Branko Saric
Keyword(s):  
Control Systems ◽  
Main Part ◽  
Fourier Transforms ◽  
Linear Time ◽  
Singular Control ◽  
Matrix Pencil ◽  
Integral Transforms ◽  
Linear Time Invariant ◽  
The Stability ◽  
Finite Fourier Transforms

The introductory part of the paper is provided to give a brief review of the stability theory of a matrix pencil for discrete linear time-invariant singular control systems, based on the causal relationship between Jordan's theorem from the theory of Fourier series and Laurent's theorem from the calculus of residues. The main part is concerned with the theory of the integral transforms, which has proved to be a powerful tool in the control systems theory. On the basis of a newly defined notion of the total value of improper integrals, throughout the main part of the paper, an attempt has been made to present the global theory of the integral transforms, which are slightly more general with respect to the Laplace and Fourier transforms. The paper ends with examples by which the results of the theory are verified.

Stability of Uncertain Linear Systems With Time Delay

1991 ◽  
Vol 113 (4) ◽  
pp. 558-567 ◽  
Author(s):  
K. Youcef-Toumi ◽  
J. Bobbett
Keyword(s):  
Time Delay ◽  
Linear Time ◽  
Sufficient Condition ◽  
Single Input Single Output ◽  
Time Delay Control ◽  
Linear Time Invariant ◽  
Single Output ◽  
Uncertain Dynamics ◽  
Delay Control ◽  
The Stability

The control of systems with uncertain dynamics and unpredictable disturbances has raised some challenging problems. This is particularly important when high system performance is to be guaranteed at all times. Recently, Time Delay Control has been suggested as an alternative control scheme. The proposed control system does not require an explicit plant model nor does it depend on the estimation of specific plant parameters. Rather, it combines adaptation with past observations to directly estimate the effect of the plant dynamics. This paper outlines the Time Delay Control law for a class of linear dynamic systems and then presents a sufficient condition for stability of linear uncertain systems with time delay. The ideas of Nyquist and Kharitonov are used in the development of a sufficient condition, which does not resort to using approximations for time delay. Like Nyquist, the condition depends on maps of the Nyquist path and, like Kharitonov, stability depends on four functions each yielding a stable system. In this paper we combine these ideas to determine the stability of systems where the Time Delay Controller is applied to single input single output, linear time-invariant plants whose coefficients are known to vary within certain defined intervals. The development is carried out in the context of Time Delay Control but it can be applied in more general cases. Two examples will illustrate the approach and the usefulness of the technique.

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